Matrix factorization is a fundamental method in statistics and machine learning for inferring and summarizing structure in multivariate data. Modern data sets often come with "side information" of various forms (images, text, graphs) that can be leveraged to improve estimation of the underlying structure. However, existing methods that leverage side information are limited in the types of data they can incorporate, and they assume specific parametric models. Here, we introduce a novel method for this problem, *covariate-moderated empirical Bayes matrix factorization* (cEBMF). cEBMF is a modular framework that accepts any type of side information that is processable by a probabilistic model or a neural network. The cEBMF framework can accommodate different assumptions and constraints on the factors through the use of different priors, and it adapts these priors to the data. We demonstrate the benefits of cEBMF in simulations and in analyses of spatial transcriptomics and collaborative filtering data. A PyTorch-based implementation of cEBMF with flexible priors is available at https://github.com/william-denault/cebmf_torch.

Bias from weak instruments may undermine the ability to estimate causal effects in instrumental variable regression (IVR). We present here a new approach to handling weak instrument bias through the application of a new type of instrumental variable coined 'Cross-Fitted Instrument' (CFI). CFI splits the data at random and estimates the impact of the instrument on the exposure in each partition. These estimates are then used to perform an IVR on each partition. We adapt CFI to the Mendelian randomization (MR) setting and term this adaptation 'Cross-Fitting for Mendelian Randomization' (CFMR). We show that, even when using weak instruments, CFMR is, at worst, biased towards the null, which makes it a conservative one-sample MR approach. In particular, CFMR remains conservative even when the two samples used to perform the MR analysis completely overlap, whereas current state-of-the-art approaches (e.g., MR RAPS) display substantial bias in this setting. Another major advantage of CFMR lies in its use of all of the available data to select genetic instruments, which maximizes statistical power, as opposed to traditional two-sample MR where only part of the data is used to select the instrument. Consequently, CFMR is able to enhance statistical power in consortia-led meta-analyses by enabling a conservative one-sample MR to be performed in each cohort prior to a meta-analysis of the results across all the cohorts. In addition, CFMR enables a cross-ethnic MR analysis by accounting for ethnic heterogeneity, which is particularly important in meta-analyses where the participating cohorts may have different ethnicities. To our knowledge, none of the current MR approaches can account for such heterogeneity. Finally, CFMR enables the application of MR to exposures that are either rare or difficult to measure, which would normally preclude their analysis in the regular two-sample MR setting.

BACKGROUND: Traditional methods for single-variant genome-wide association study (GWAS) incur a substantial multiple-testing burden because of the need to test for associations with a vast number of single-nucleotide polymorphisms (SNPs) simultaneously. Further, by ignoring more complex joint effects of nearby SNPs within a given region, these methods fail to consider the genomic context of an association with the outcome. RESULTS: To address these shortcomings, we present a more powerful method for GWAS, coined 'Wavelet Screening' (WS), that greatly reduces the number of tests to be performed. This is achieved through the use of a sliding-window approach based on wavelets to sequentially screen the entire genome for associations. Wavelets are oscillatory functions that are useful for analyzing the local frequency and time behavior of signals. The signals can then be divided into different scale components and analyzed separately. In the current setting, we consider a sequence of SNPs as a genetic signal, and for each screened region, we transform the genetic signal into the wavelet space. The null and alternative hypotheses are modeled using the posterior distribution of the wavelet coefficients. WS is enhanced by using additional information from the regression coefficients and by taking advantage of the pyramidal structure of wavelets. When faced with more complex genetic signals than single-SNP associations, we show via simulations that WS provides a substantial gain in power compared to both the traditional GWAS modeling and another popular regional association test called SNP-set (Sequence) Kernel Association Test (SKAT). To demonstrate feasibility, we applied WS to a large Norwegian cohort (N=8006) with genotypes and information available on gestational duration. CONCLUSIONS: WS is a powerful and versatile approach to analyzing whole-genome data and lends itself easily to investigating various omics data types. Given its broader focus on the genomic context of an association, WS may provide additional insight into trait etiology by revealing genes and loci that might have been missed by previous efforts.

BACKGROUND: We present here a computational shortcut to improve a powerful wavelet-based method by Shim and Stephens (Ann Appl Stat 9(2):665-686, 2015. https://doi.org/10.1214/14-AOAS776 ) called WaveQTL that was originally designed to identify DNase I hypersensitivity quantitative trait loci (dsQTL). RESULTS: WaveQTL relies on permutations to evaluate the significance of an association. We applied a recent method by Zhou and Guan (J Am Stat Assoc 113(523):1362-1371, 2017. https://doi.org/10.1080/01621459.2017.1328361 ) to boost computational speed, which involves calculating the distribution of Bayes factors and estimating the significance of an association by simulations rather than permutations. We called this simulation-based approach "fast functional wavelet" (FFW), and tested it on a publicly available DNA methylation (DNAm) dataset on colorectal cancer. The simulations confirmed a substantial gain in computational speed compared to the permutation-based approach in WaveQTL. Furthermore, we show that FFW controls the type I error satisfactorily and has good power for detecting differentially methylated regions. CONCLUSIONS: Our approach has broad utility and can be applied to detect associations between different types of functions and phenotypes. As more and more DNAm datasets are being made available through public repositories, an attractive application of FFW would be to re-analyze these data and identify associations that might have been missed by previous efforts. The full R package for FFW is freely available at GitHub https://github.com/william-denault/ffw .